Reinforcing layers such as reinforcing braid layers can provide thin-walled catheters with desired resistance to kinking while retaining desirable flexibility. Some reinforcing braids, such as tempered or high tensile stainless steel braids, can be susceptible to braid wire flaring in which unrestrained ends of the braid bend outward. Various techniques have been proposed for dealing with braid wire flaring, including the use of heat treatment processes on the braid, braid constraints and adhesives. Nevertheless, a need remains for improved methods of producing catheters having reinforcing braids while preventing or substantially preventing braid wire flaring without thickening the top layer or heat-treating the reinforcing braid material. A need also remains for a braid-reinforced catheter that has a well-bonded soft distal tip without use of adhesives.